A memetic algorithm for minimizing the total weighted completion time on a single machine under linear deterioration

In this paper, we consider the problem of minimizing the total weighted completion time on a single machine. Jobs processing times are increasing linear function of start times. First, we present some new dominance properties for this NP-hard problem. And next, using these properties, we develop a memetic algorithm for the problem. The results of computational experiments show the good performance of the proposed algorithm.